Chemical Futures &Options Inc Speaker MIDDLE EAST SEMINAR BAHRAIN 1995 Stephen Hulme VP 1January 18/19

Chemical Futures &Options Inc


Speaker

MIDDLE EAST SEMINAR MIDDLE EAST SEMINAR BAHRAIN 1995BAHRAIN 1995

Stephen Hulme VP

1January 18/19


The construction of Synthetic Swaps using 3 Month futures

strips

• In developed financial markets with a liquid futures markets the LIBOR cash curve is driven by short term futures contracts. For most major currencies (US$, Yen, Sterling, Deutschemarks etc.) contracts exist that are based on LIBOR.

• Using the LIBOR cash curve Forward Rate Agreements (FRA’s) are priced.

Introduction

2


• Since Interest Rate Swaps define a set of cash exchanges in the future they can be decomposed into a series of FRA’s: an FRA corresponding to each cash exchange in the future.

• Given that FRA pricing is driven by exchange traded futures, Swap pricing will also be derived from the futures market.

• All swaps that fall within the time horizon of liquid futures contracts will be priced and valued based on those futures contracts.

3


• FRAs and interest rate swaps are both interest derivative products that lock in a fixed rate for a specific period of time.

• A FRA can be thought of as a single period forward swap and a swap can be thought of as a series of FRAs strung together

• Given a calculated fixed rate of a string of FRAs the same as the OTC fixed rate swap the trader can be indifferent between the two alternatives

• Because FRAs are determined by exchange traded futures contracts, an interest rate swap can also be constructed out of a series of exchange traded futures contracts

4


2 Yr $ 100 Million loan paying interest every six months at a

rate equivalent to the six month Libor rate

13-Oct-94

13-Apr-95 13-Oct-95 15-Apr-96 14-Oct-96

0 x 6

6 x 12 12 x 18 18 x 24

Months

2418126

5


• To hedge the exposure completely, we need to fix the future six month LIBOR rate for periods 6x12, 12x18 and 18x24.

• There is no interest rate exposure for period 0x6 because the rate for this period is the six month cash rate

• To hedge the exposure we can buy three FRAs: 6x12, 12x18 and 18x24.

• The all in rate achieved by buying the series of FRAs and the cash instrument is derived by compounding the rates for each of the four periods.

• Since FRAs are determined by futures contracts the interest rate swap can be constucted as follows

6


IMM FRA Calculations

Future 1

Future 2

Future 3

Future 4

Future 5

Future 6

Future 7

Future 8

9407

9370

9329

9298

9267

9260

9247

9236

Dec-94

Mar-95

Jun-95

Sep-95

Dec-95

Mar-96

Jun-96

Sep-96

IMM FRA's

2 X 5 5.930%

5 X 8 6.300%

8 X 11 6.710%

11 X 14 7.020%

14 X 17 7.330%

17 X 20 7.400%

20 X 23 7.530%

23 X 26 7.640%

1.0150

1.0147

1.0183

1.0177

1.0185

1.0187

1.0190

1.0193

IMM Discount DaysFactors

9184

98

91

91

91

91

91note 1 note 2 note 3

note 1 = (10000 - future price) / 10000

note 2 = 1 +((Fut days / 360)*IMM FRA Rate )

note 3 = Days in Future Month7


3 Mth FRA Days Calculation

Spot: 13-OctSpot Runs3 Mth

6 x 9

9 x 1212 x 1515 x 18

18 x 21

21 x 24

13-Apr-95 -13-Jul-95 -

9113-Oct-9513-Jul-95

9213-Oct-95 -15-Jan-96 -

9415-Jan-96

15-Apr-96 9115-Apr-96 -15-Jul-96 -

9115-Jul-96 14-Oct-96 91

8


6 Mth FRA Days Calculation


0 x 6 6 x 1212 x 18

18 x 24

13-Oct-94 -13-Apr-95 -

18213-Oct-9513-Apr-95

18313-Oct-95 - 15-Apr-96 185

15-Apr-96 - 18214-Oct-96

Total : 7329


IMM & SPOT FRA DAY COUNT CALENDAR

13-Oct-94 13-Apr-95 -

Future 222-Mar-95

13-Jul-95 13-Oct-95 15-Jan-96 15-Apr-96 15-Jul-96 14-Oct-96

14-Jun-95Future 3

20-Sep-95Future 4

20-Dec-95Future 5

20-Mar-96Future 6

19-Jun-96Future 7

18-Sep-96Future 8

2962

84 98 91 91

69 23 68 26 65 26

91

65

91

26 65 26

91

6 x 9

0 x 6

9 x 12

6 x 12

12 x 15

12 x 18

15 x 18 18 x 21 21 x 24

18 x 24

10


SPOT FRA DISCOUNT FACTORS

Future 1Future 2Future 3Future 4Future 5Future 6Future 7Future 8

6x91.0000001.0108291.0053711.0000001.000000

9x121.0000001.0000001.0128261.0044561.0000001.000000

12x151.0000001.0000001.0000001.0132301.0052591.0000001.000000

15x18

1.0000001.0132001.0053091.0000001.000000

18x21

1.0000001.0000001.0133261.0054021.0000001.000000

21x24

1.0000001.0000001.0135591.0054801.0000001.000000

note 1

note 1: IMM discount factor future 2 ^ (62/84) = 1.010829

IMM discount factor future 3 ^ (29/98) = 1.005371

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91919294919191

6.432 % = ((1.010829*1.005371) -1)*360/91

6.785 % = ((1.012826*1.004456) -1)*360/92

Days


6 x 9 9 x 1212 x 1515 x 1818 x 2121 x 24

Rate

7.108 % = ((1.013230*1.005259) -1)*360/94

7.350 % = ((1.013200*1.005309) -1)*360/91

7.437 % = ((1.013326*1.005402) -1)*360/91

7.561 % = ((1.013559*1.005480) -1)*360/91

3 Mth. FRA Calculation3 Mth. FRA Calculation

12


5.750 % = spot rate

Days

Spot: 13-Oct

6 Mth. FRA Calculation6 Mth. FRA Calculation

182182

183

185

182

Spot Runs

6 Mth

0 x 6

6 x 12

12 x 18

18 x 24

Rate

6.665 % = ((1+(91/360*6.432%))*(1+(92/360*6.785%))) - 1 / ((91+92)/360)

7.294 % = ((1+(94/360*7.108%))*(1+(91/360*7.350%))) - 1 / ((94+91)/360)

7.570 % = ((1+(91/360*7.437%))*(1+(91/360*7.561%))) - 1 / ((91+91)/360)

13


Compounded 2 Yr. Fixed Rate

5.750%

6.665%

7.294%

7.570%

Invest $1.0291

Invest $1.0639

Invest $1.1037

13-Oct-94

13-Apr-95 - 13-Oct-95 15-Apr-96 14-Oct-96

0 x 6

6 x 12 12 x 18 18 x 24

Invest $1.0000

Return $1.0291

Return $1.0639

Return $1.1038

Return $1.1460

2 yr. effective fixed rate (A/360) = (1+(6Mth Libor*182/360))

* (1+ (6x12 FRA*183/360))

* (1+ (12x18 FRA*185/360))

* (1+ (18x24 FRA*182/360))

- 1 = 14.61%14


Conversion of 2 Yr effective rate to semi annual bond

equivalent yield (BEY)

Decompound to 182.5 days (semiannual) : 182.5

Divide by total number of days /732

= 0.2493

Raise 2 Yr eff. rate to resulting exponent [y^x] 1.1460^0.249

Subtract 1 = 0.0346

Annualise this result : 0.0346*365

= 12.6122

Divide by 182.5 12.6122/182.5

= 6.9108% BEY (Synthetic 2 Yr Swap Rate)15


Allocation of Contracts to hedge BEY Swap Rate

Here we are going to look at an approach that hedges against changes in the cash flow rather than changes in the net present value of the swap. Consider our simple generic swap. The first net cash payment is fixed at the time the deal is struck. The next three net payments depend on realised values of six month Libor. In each case, the nominal value of a basis point change in six month Libor for a $100 million swap is $5000 if the actual number of days between payments is180.

16


Hedging the Legs of a Swap

The present value of these changes, however, depend on term Libor to each payment. The first uncertain payment is made in twelve months, the second in eighteen, and the third in twenty four. Given the futures derived zero coupon money market rates that we have used in our swap example , the values of twelve, eighteen and twenty four month Libor we would need to discount these nominal cash flows are:

17


Implied Libor discount rates

R12 = 100 * (( 1+(0.057500 * 182/360)) * ( 1+(0.06650 * 183/360)) - 1) * 360/365 = 6.3025%

R18 = 100 * (( 1+(0.063025 * 365/360)) * ( 1+(0.07294 * 185/360)) - 1) * 360/550 = 6.7942%

R24 = 100 * (( 1+(0.067942 * 550/360)) * ( 1+(0.07570 * 182/360)) - 1) * 360/732 = 7.1852%

Given these term Libor rates, the present value of a day count adjusted $5000 change in each of the uncertain cash flows is:

18


Present value of a 1bp rate change for each future

PV02 (F2) : (62/360*10000)/(1+(0.063025*365/360)) = 1618.78

PV03 (F3) : (98/360*10000)/(1+(0.063025*365/360)) = 2558.72

PV04 (F4) : (23/360*10000)/(1+(0.063025*365/360)) = 600.52

12 x 18

6 x 12

PV04 (F4) : (68/360*10000)/(1+(0.067942*550/360)) = 1711.26

PV05 (F5) : (91/360*10000)/(1+(0.067942*550/360)) = 2290.07

PV06 (F6) : (26/360*10000)/(1+(0.067942*550/360)) = 654.31

18 x 24

PV06 (F6) : (65/360*10000)/(1+(0.071852*732/360)) = 1575.39

PV07 (F7) : (91/360*10000)/(1+(0.071852*732/360)) = 2205.50

PV08 (F8) : (26/360*10000)/(1+(0.071852*732/360)) = 630.16 19


Derived Futures Strip 2 Yr Swap

Future 1

Future 2

Future 3

Future 4

Future 5

Future 6

Future 7

Future 8

Dec-94

Mar-95

Jun-95

Sep-95

Dec-95

Mar-96

Jun-96

Sep-96

= $2558.72 / $25 = 102.35 contracts

= $1618.78 / $25 = 64.75 contracts

= $2311.78 / $25 = 92.47 contracts

= $2290.07 / $25 = 91.60 contracts

= $2229.70 / $25 = 89.19 contracts

= $2205.50 / $25 = 88.22 contracts

= $ 630.16 / $25 = 25.21 contracts

Total = 553.79 contracts20


SUMMARY

• A synthetic swap with a fixed rate of 6.9108% (BEY) has been constructed from a strip of exchange traded futures contracts.

• Given an efficient market the cost of this strip versus the OTC interest rate swap should be cheaper to hedge the original 6 Month LIBOR reset exposure over 2 years due to narrow bid and ask spreads.

• Because futures markets are extremely liquid and transaction costs are low barriers to opening and closing positions are low

21


Futures Sales Contacts

• Chicago: Mark Psaltis VP, Ph. 312 726 9250

• London : Stephen Hulme VP, Ph. 071 777 4419

• Philadelphia : Bob Damerjian VP, Ph. 215 561 3030

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The information herein has been obtained from sources believed to be reliable, but Chemical Futures & Options, Inc (CF&O) does not warrant its completeness or accuracy nor shall it be liable for damages arising out of any person’s reliance thereon. Prices, opinions and estimates reflect CF&O’s judgement on the date hereof and are subject to change without notice. Nothing contained herein shall be construed as an offer to buy or sell any commodity, security, option or futures contract. CF&O is a separately incorporated, wholly owned subsidiary of Chemical Banking Corporation. Member NASD/NFA/SFA. All rights reserved c 1995.

Documents

Chemical Futures &Options Inc Speaker MIDDLE EAST SEMINAR BAHRAIN 1995 Stephen Hulme VP 1January 18/19